Question

1. right triangle abc has legs of 24 and 7. what is the sin of the triangles smallest angle?

f. $\frac{7}{24}$
g. $\frac{25}{7}$
h. $\frac{24}{25}$
i. $\frac{25}{24}$
k. $\frac{7}{25}$

Explanation:

Step1: Find hypotenuse via Pythagoras

$$c = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$$

Step2: Identify smallest angle's opposite side

Smallest angle faces shortest leg (length 7).

Step3: Compute sine of smallest angle

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{7}{25}$

Answer:

K. $\frac{7}{25}$